On the Implicit Bias of Linear Equivariant Steerable Networks

Understand

We study the implicit bias of gradient flow on linear equivariant steerable networks in group-invariant binary classification.

• Our findings reveal that the parameterized predictor converges in direction to the unique group-invariant classifier with a maximum margin defined by the input group action.
• Under a unitary assumption on the input representation, we establish the equivalence between steerable networks and data augmentation.
• Furthermore, we demonstrate the improved margin and generalization bound of steerable networks over their non-invariant counterparts.